16. Adam uses a microscope to observe insects in science class. The
microscope enlarges objects to 100 times their actual size. Find the length of
each insect as seen in the microscope.
A=
cm
(Type a whole number or a decimal.)

Answer:

The side lengths are 5, 12, 13

Step-by-step explanation:

These are the side lengths we know before we have solved the problem.

a= x   b= x+7   c= 13

If we put this into the Pythagorean theorem, we get

[tex]13^{2} = x^{2} +(x+7)^{2}[/tex]

Expand

[tex]169 = 2x^2+14x+49\\[/tex]

Subtract 169 from both sides

[tex]0 =2x^2+14x-120[/tex]

Solve using the quadratic formula

a= 2   b= 14   c= -120

[tex]\frac{-14\pm \sqrt{14^2-4\cdot \:2\left(-120\right)}}{2\cdot \:2}[/tex]

[tex]x= \frac{-14\pm \:34}{2\cdot \:2}[/tex]  

If we separate the solutions we get

[tex]x= \frac{20}{4} = 5[/tex]

and

[tex]x= \frac{-48}{4} = -12[/tex]

Since this is a question about length, we can ignore the negative.

So the longer leg is 12ft and the shorter leg is 5ft

The shorter length is 5feet and the longer length is 12 feet

Let the shorter leg = x

Let the longer leg = x+7

Therefore,

x² + (x+7)² = 13²

x² + x² + 14x + 49 = 169

Collect like terms

2x² + 14x + 49 - 169 = 0

2x² + 14x - 120 = 0.

Divide by 2

x² + 7x - 60

By using quadratic equation

x² + 12x - 5x - 60

x(x + 12) - 5(x + 12)

Therefore, x - 5 = 0

x = 0 + 5.

x = 5

The shorter length is 5ft

Longer length = 5+7 = 12 feet

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Answer:

Step-by-step explanation:

9(2n + 1)

use the distributive property a(b + c) = ab + ac

= (9)(2n) + (9)(1) = 18n + 9

Step-by-step explanation:

9(2n+1) =0

18n+9 = 0

18n = -9

n = -9/18

n = -1/2

Answer:

y=4/3x-7

Step-by-step explanation:

The slope intercept formula y=mx+b, m being the slope and b being the y-intercept so all we have to do is find those and plug them in to get the answer.

Answer:

-300

Step-by-step explanation:

z = -21/0.07

z = -300

Answer:

-300

Step-by-step explanation:

Divide -21 by 0.07 to get -300

Answer: since the toy is marked down 15%,

you do p*.85  

to find the remaining cost

Step-by-step explanation: I got this from a friend. But I hope this helps! <3

Answer:

$15

Step-by-step explanation:

The unit rate or how much a comic book costs = total cost ÷ number of comic books

Using any given pair, let's use the first row (3, 3.75):

Unit rate = [tex] \frac{3.75}{3} = 1.25 [/tex]

This means a comic book cost $1.25.

Therefore, 12 comic books would cost:

12 × 1.25 = $15

Answer:

-5.5

Step-by-step explanation:

Answer:

Given - Angles measure 2x , X and 3x

To find - Measures of 2x

Solution -

2x + X = 180° ( forming linear pair )

3x = 180°

x = 180/3

x = 60°

2x = 2 × 60 = 120°

Answer:

120°

plz give brainlist

Step-by-step explanation:

since 2x and x form a straight angle you get the equation

2x + x = 180

combine like terms

3x = 180

devide by 3

x = 60

evaluate 2x

2(60) = 120

Answer:

21

Step-by-step explanation:

you plug in 5 for a and 6 for b and solve.

The value of the expression 3 + (a + 4)(8 - b) when a = 5 and b = 6 is 21

3 + (a + 4)(8 - b)

when,

a = 5 and b = 6

= 3 + (5 + 4) (8 - 6)

= 3 + 9 (2)

= 3 + 18

= 21

Therefore, the value of the expression 3 + (a + 4)(8 - b) when a = 5 and b = 6 is 21

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Answer:

60 years

Step-by-step explanation:

Given that :

Sarah's age = a

Assume Sarah is older than 44 ; then a > 44

64 = 4 times difference between a and 44

Expressing the problem mathematically ;

64 = 4 * (a - 44)

64 = 4a - 176

64 + 176 = 4a

240 = 4a

a = 240 / 4

a = 60

Hence, Sarah is aged 60

Answer:

do u know the answer ik it's five units up but that it

Answer: a vertical stretch with a scale factor of 2. and a translation of 5 units up.

Step-by-step explanation:

Answer:

What's the triangle though?

Step-by-step explanation:

Answer:

Not enough Data

Step-by-step explanation:

Answer:

I honeslty dont know I just need points to answer a question

Step-by-step explanation:

hope you find the answer youre looking for!

Putting money into more than one kind of investment at a time is called Diversification.

This a technique which helps to reduce risk through investing in different sectors and opportunities.

It also involves putting money in more than one type of investment which makes Diversification the most appropriate choice.

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Answer:

I’m sorry but I can’t see how much it’s on sale for so just tell me and I’ll answer.

Step-by-step explanation:

Answer:

Use this

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

all should add up to 180

Answer:

E. 70°, 60°, 40°​        D. 75°, 50, 100        C. 50°, 50°, 100°

Step-by-step explanation:

If you add the three degrees together, they all should equal 180 degrees.

Hope this helped :)

Answer:

the perimeter of a square with sides 2.5 mm long is b.10 mm.

Answer:

4

Step-by-step explanation:

Answer:

5 and 1/2

Step-by-step explanation:

Answer: X= 108125 and  Y  = 373125.

Step-by-step explanation:

Given system :

[tex]X= 33500+0.2Y (i)\\\\ Y=26500+0.1X (ii)[/tex]

Consider (ii)

[tex]Y=26500+0.1X\\\\\Rightarrow\ Y-0.1X=26500[/tex]

Multiply 10 on both sides , we get

[tex]10Y-X=265000 (iii)[/tex]

Add (i) and (iii)

[tex]10Y= 33500+26500+0.2Y\\\\\Rightarrow\ 10Y-0.2Y= 298500\\\\\Rightarrow\ 0.8Y= 298500\\\\\Rightarrrow\ Y=\dfrac{298500}{0.8}\\\\\Rightarrrow\ Y=373125[/tex]

Put this in (i)

[tex]X= 33500+0.2(373125) =108125[/tex]

Hence, X= 108125 and  Y  = 373125.

Answer:

95.83%

Step-by-step explanation:

Answer:

[tex]Mean = 42[/tex]

Step-by-step explanation:

Given

Represent Fred with F; Norman with N and Dave with D.

[tex]Total = 128[/tex]

[tex]D = 44[/tex]

Required

Determine the arithmetic mean of F and N

First, we have that:

[tex]F + N + D = 128[/tex]

Substitute 44 for D

[tex]F + N + 44 = 128[/tex]

Subtract 44 from both sides

[tex]F + N + 44 - 44 = 128 - 44[/tex]

[tex]F + N = 84[/tex]

Arithmetic mean of F and N is calculated as follows:

[tex]Mean = \frac{F + N}{2}[/tex]

[tex]Mean = \frac{84}{2}[/tex]

[tex]Mean = 42[/tex]

Answer:

5 weeks

Step-by-step explanation:

319.50-21.95=297.55

297.55/63.00=4.72

Since he can't wait for those many weeks, you would round it to 5 so he has enough money

Answer:

4

Step-by-step explanation:

2/5 is the same as 4/10

Answer:

Y=3.68x

Step-by-step explanation:

Answer:

Its should be y=$3.68(X)

Answer:

1.08

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

1.01<1.08<1.17<1.20